The dispensing of stored liquids from, for example, small hand-held dispensers commonly activated by selective manual pressing or squeezing or manipulation of a flexible wall portion or feature or the like of the dispenser has become a ubiquitous way of making selective use of a wide variety of liquids of all viscosities, from extremely “thin” or water-like liquids such as scented toilet water to highly viscous liquids such as toothpaste. A common problem that arises in the use of such dispensers is that, as the dispenser is manipulated to open the valve—which is normally closed to prevent leakage when not in use—so as to release a desired amount of the stored liquid and to then cause or allow the valve to close, some amount of the released or dispensed liquid often remains on the surface areas of and about the dispensing opening of the valve. It is not uncommon, particularly with increasing viscosity of the liquid, for increasing amounts of the dispensed liquid to collect and remain on and about the outlet of the dispenser. The presence of this excess liquid is unsightly, unhealthy and can interfere with the ability of the valve to fully close and/or the functioning of the valve insofar as allowing selective user control of the dispensing operation. Previous efforts to avoid this problem, as by attempting to cause such excess liquid to be “sucked back” into the dispenser as the valve closes, for example by increasing the force by which the valve closes (and correspondingly, that required to open the valve), have merely made such dispensers more difficult to operate without significantly alleviating this issue.